Orbital stability analysis around the primary of a binary asteroid system

Unlike most previous studies that focused on libration point orbits, we investigate perturbed Keplerian orbits around the primary of a binary asteroid system, with the gravity of the secondary modelled as the third-body perturbation. The orbital stability around the primary is studied by using semi-analytical techniques from the aspect of the long-term oscillation of eccentricity. Our previous numerical investigations indicate that the eccentricity undergoes a large-amplitude long-period oscillation, which is caused by the secular perturbation of the secondary's gravity and may cause impact on the primary's surface. To study this problem, a two-degree-of-freedom orbital dynamics model, based on the newly proposed doubly-averaged, semi-analytical orbital dynamics incorporating effects of the primary's oblateness and the secondary's non-spherical third-body gravity, is described. This solution is used to investigate the oscillation of the eccentricity, including its phase and amplitude, and the dependence on the initial orbital geometry. The analytical results can reveal the origin of the instability, predict stable and unstable regions in the space of orbital elements, and determine the initial orbital geometry that can ensure the secular stability. The binary asteroid system 2003 YT1 is used as an example to present our verifications and analysis. The analytical results can also be applied to other binary asteroid systems and even planetary systems if the central body's oblateness and the third-body gravity dominate the perturbations.